Year: 2026
Type: preprint
Abstract: We study the linear energetic stability of non-Abelian vortices in an $SO(3)$ gauge-Higgs theory with residual gauge group $A_4$. In our previous work, we identified two families of such vortices associated with order-two and order-three elements of $A_4$, and found Bogomol'nyi--Prasad--Sommerfield-like behavior at special ratios of the Higgs and gauge-boson mass scales. Here, we investigate their stability against $SO(3)$ gauge and Higgs perturbations by analyzing the second order variation of the vortex tension using analytical and numerical methods. In particular, when all relevant mass scales are equal, we prove linear stability for all vortices in the order-three family. By contrast, at the same mass point, we prove that a vortex in the order-two family is unstable. Thus, although both vortex families exhibit Bogomol'nyi--Prasad--Sommerfield-like behavior in their reduced equations at this mass point, their stability properties in the full $SO(3)$ theory are qualitatively different.
Source: arXiv (Cornell University)
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Award: G5667790117
OpenAlex ID: W7222175903